Dynamics of Fluctuactions in the BCS-BEC Crossover in Superfluid Fermi Gases

The BCS-BEC crossover phenomenon in a 3D attractive Fermi gas is revisited by using finite temperature Green functions formalism derived from the quantum path integral technique and Mean Field Approximation (MFA). Collective modes for weak and strong coupling particle-particle interaction g are obtained after recovering the dynamical coefficients in the non-linear Time Dependent Ginzburg Landau (TDGL) equation, and numerically simulated under those particular states for the filling energy mu similar to 0 and order parameter Delta (x, tau) similar to Delta(0). Explicit formulas for the first order average fluctuations <eta(2)(q,w)> and the scaling law for the thermal energy associated to the non-linear collective modes are also reported.